net.mumie.mathletfactory.math.number.numeric

Class Span

java.lang.Object

net.mumie.mathletfactory.math.number.numeric.Span

public class Span
extends java.lang.Object

This class determines the span of an arbitrary number of vectors given as NumberTuples. This can be done by returning a new set of basis vectors (the pivot columns of corresponding the echelon form) or simply the indices (with respect to argument array), which of the given vectors would serve as a basis.

Author:

Paehler

Document status:

finished

Constructor Summary

Constructors

Constructor and Description
Span()

Method Summary

Methods

Modifier and Type	Method and Description
static NumberTuple[]	getBasisForSpanOf(NumberTuple[] aListOfVectors) This method returns for an arbitrary array of NumberTupels a (deep-copied) subset that serves as a basis for the Span of aListOfVectors
static boolean	isContainedInSpanOf(NumberTuple testVector, NumberTuple[] testSpan) This method tests, if a vector is contained in the Span of other vectors.
static AffinePoint[]	span(AffinePoint[] points) Deprecated. may be removed in future versions!
static NumberTuple[]	span(NumberTuple[] vectors) This method returns a basis for the span of the given NumberTupels (vectors).
static int[]	spanIndices(NumberTuple[] vectors) This method returns the indices of the argument vectors, that would serve as a basis for the span (e.g. if the argument was arg={{1,0, 0}, {2, 0, 0}, {0, 0, 1}}, the int[] {0,2} would be returned, because the first and the third vector serve as a basis for the span(arg).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Span

public Span()

Method Detail

span

public static NumberTuple[] span(NumberTuple[] vectors)

This method returns a basis for the span of the given NumberTupels (vectors). This is done by constructing the matrix, of which the row-equivalent echelon form is calculated. The columns of the echelon form matrix containing the pivot elements are assigned as the new basis vectors, which are returned as NumberTupels.

Parameters:

vectors - a NumberTuple[], the vectors of which the span is constructed.

Returns:

a NumberTuple[], the basis of the span.

span

public static AffinePoint[] span(AffinePoint[] points)

Deprecated. may be removed in future versions!

Determine the span of an array of affine points by regarding them as projective vectors.

spanIndices

public static int[] spanIndices(NumberTuple[] vectors)

This method returns the indices of the argument vectors, that would serve as a basis for the span (e.g. if the argument was arg={{1,0, 0}, {2, 0, 0}, {0, 0, 1}}, the int[] {0,2} would be returned, because the first and the third vector serve as a basis for the span(arg).

getBasisForSpanOf

public static NumberTuple[] getBasisForSpanOf(NumberTuple[] aListOfVectors)

This method returns for an arbitrary array of NumberTupels a (deep-copied) subset that serves as a basis for the Span of aListOfVectors

isContainedInSpanOf

public static boolean isContainedInSpanOf(NumberTuple testVector,
                          NumberTuple[] testSpan)

This method tests, if a vector is contained in the Span of other vectors.